I believe that (b) should be this......
23% of the customers purchased a smartphone....of these, 12% paid online......so
The % of total customers that purchased a smartphone AND paid online =
12% of 23% = .12 * .23 = about 2.76% of the total customers
(c) Let A be the probability that a customer purchased a smartphone = .23
Let B be the probability that a customer paid on line = ..08
Let P(A and B) = .0276
So
P( A or B) = P(A) + P(B) - P(A and B) =
.23 + .08 - .0276 =
.2824 =
about 28.24% of the total customers purchased a smartphone or paid online
(d) The events buying a smartphone and paying online aren't mutually exclusive, brcause we could have purchased a smartphone and paid online
(e) If P(A and B) = P(A) * P(B) .....then the events are independent
So
P(A and B) = .0276
P(A) = .23
P(B) = .08
But
.0276 = .23 * .08 ???
.0276 = .0184
So.....these events are not independent
